vault backup: 2025-11-12 17:02:15

.obsidian/workspace.json

@@ -62,37 +62,9 @@
               "icon": "lucide-file",
               "title": "Trigonometri"
             }
-          },
-          {
-            "id": "be47d5ede3a9176b",
-            "type": "leaf",
-            "state": {
-              "type": "markdown",
-              "state": {
-                "file": "Komplexa tal.md",
-                "mode": "source",
-                "source": false
-              },
-              "icon": "lucide-file",
-              "title": "Komplexa tal"
-            }
-          },
-          {
-            "id": "76c8d943958d45bf",
-            "type": "leaf",
-            "state": {
-              "type": "markdown",
-              "state": {
-                "file": "Gräsvärde (1).md",
-                "mode": "source",
-                "source": false
-              },
-              "icon": "lucide-file",
-              "title": "Gräsvärde (1)"
-            }
           }
         ],
-        "currentTab": 5
+        "currentTab": 3
       }
     ],
     "direction": "vertical"
@@ -252,17 +224,17 @@
       "obsidian-git:Open Git source control": false
     }
   },
-  "active": "76c8d943958d45bf",
+  "active": "e616c86f78b96cf1",
   "lastOpenFiles": [
-    "gv1.png",
-    "Funktioner.md",
-    "Funktioner Forts.md",
-    "Gräsvärde (1).md",
-    "Komplexa tal.md",
-    "Grafer.md",
-    "Trigonometri.md",
     "k2.png",
     "k1.png",
+    "gv1.png",
+    "Komplexa tal.md",
+    "Gräsvärde (1).md",
+    "Funktioner Forts.md",
+    "Trigonometri.md",
+    "Grafer.md",
+    "Funktioner.md",
     "f_inverse.png",
     "g2.png",
     "g1.png",

Trigonometri.md

@@ -6,6 +6,10 @@
 	- Ex: $$\begin{align}180^\circ=\pi\text{ rad}\\\frac{\pi}{3}\text{ rad}=30^\circ\\\frac{\pi}{4}\text{ rad}=45^\circ\\\frac{\pi}{3}\text{ rad}=60^\circ\\\frac{\pi}{2}\text{ rad}=90^\circ\\2\pi\text{ rad}=360^\circ\end{align}$$
 - The right angled triangle
 	- **Def**: *The trigonometric functions: *$$\begin{align}\sin\theta=\frac{\text{perpendicular}}{\text{hypotenuse}}\\\cos\theta=\frac{\text{base}}{\text{hypotenuse}}\\\tan\theta=\frac{\text{perpendicular}}{\text{base}}\end{align}$$
+	- In addition to above, $\csc\theta=\frac{1}{\sin\theta},\sec\theta=\frac{1}{\cos\theta},\cot\theta=\frac{1}{\tan\theta}$
+	- Pythagoras' formula: $p^2+b^2=h^2$
+	  which leads to the **trigonometric identity**: $\sin^2\theta+\cos^2\theta=1$
+	  and also $\tan^2\theta+1=\sec^2\theta$
 	- Dominains and ranges:
 		- $D_{\sin}=\mathbb{R}\;\;R_{\sin}=[-1,1]$
 		- $D_{\cos}=\mathbb{R}\;\;R_{\cos}=[-1,1]$